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\begin{document}

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\begin{poster}{
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{
\begin{minipage}{13em}
	\includegraphics[width=1.5in]{sc.jpg}
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}
{
The Semi-Constrained Court: \hspace{2mm} \LARGE{Replicating and Extending Hall (2014)}
}
{\vspace{4mm}
\LARGE{\textbf{Moohyung Cho}}\hspace{2mm} -- \hspace{2mm} Duke University, \hspace{1mm} mc426@duke.edu
}
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\headerbox{Original Paper: Hall (2014)}{name=introduction,column=0,row=0,span=1}
{
% %\section*{Source}
% %Henne, Peter S. 2012. ``The Two Swords: Religion-state connections and interstate disputes." \emph{Journal of Peace Research}. 49(6):753-768.
   	\vspace{2mm}
   		\begin{adjustwidth}{2mm}{2mm}
   			 \textbf{Research Question}
   	\begin{itemize}
   		\item[] When is the Supreme Court constrained by external pressures (e.g. public opinion and elite preferences)?
   \end{itemize} 
   \vspace{3mm}
   \textbf{Summary}
   \begin{itemize}
   	   \item[] Hall (2014) investigates the influence of public opinion and elite preferences on the Court's decision to invalidate federal statutes. He finds that these external forces have \textbf{differential effects in different issue contexts}. While the Court enjoys greater implementation power in \emph{vertical} cases, she is strongly constrained in \emph{lateral} cases, whose implementation depends on the support from non-judicial actors.
   \end{itemize}
\end{adjustwidth}

   \vspace{2mm}
}
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\headerbox{Research Design}{name=data,column=0,below=introduction,span=1}
{   	\vspace{2mm}
	\begin{adjustwidth}{2mm}{2mm}
\textbf{Data}
\begin{itemize}
	\item[] The Supreme Court's decision-making in 174 cases in which a party challenged the constitutionality of a federal statute between 1955 and 2004. 
	\\ (83 lateral cases and 91 vertical cases)
\end{itemize}
\vspace{3mm}\textbf{Dependent Variable}
\begin{itemize}
	\item[] \textbf{Invalidation of Federal Law by the Court}
	\subitem 1 = Invalidation (47 cases)
	\subitem 0 = No Invalidation (127 cases)
\end{itemize}
\vspace{3mm}
\textbf{Main Independent Variables}
\begin{enumerate}
	\item \textbf{Strike Mood} \\Public opinion about the invalidation
	\item \textbf{Institutional Constraint} \\Elite preferences about the invalidation
\end{enumerate}
\vspace{3mm}  
\textbf{Method} \hspace{4mm} Multivariate logistic regression		
	\end{adjustwidth}
   	\vspace{2mm}   
}

%
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\headerbox{Vertical Cases vs. Lateral Cases}{name=case,column=0,below=data,span=1}
{   	\vspace{2mm}
	\begin{adjustwidth}{2mm}{2mm}
	\textbf{Vertical Cases}
	\begin{itemize}
		\item[] Administered through the judicial system so that lower courts can directly implement policy change. (e.g. criminal law, civil liability, and judicial administration)
	\end{itemize}
	\textbf{Lateral Cases}
	\begin{itemize}
		\item[] Implemented by elected officials outside the judicial hierarchy so that lower-court judges play no inherent role in policy process. The efficacy of their rulings relies on non-judicial actors. (e.g. education and governmental agencies)		
	\end{itemize}
\end{adjustwidth}
   	\vspace{2mm} 
}

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\headerbox{Estimates of the Model}
{name=results,column=1,span=1}
{\vspace{2mm}
\centering
\smaller{\textbf{The Differential Impact of Supreme Court Constraint \\on Judicial Review}}\\
\includegraphics[width=.994\linewidth]{coefplot.pdf}
\begin{quote}
	\textit{Note}: For presentation purpose, I scaled some variables with high estimates: $\frac{1}{100}$ for Institutional Constraint in lateral cases; $\frac{1}{10}$ for Institutional Constraint and Floor Median Distance from Court. I also excluded intercept and four control variables of the model in this coefficient plot.
\end{quote}
\vspace{2mm}
}

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\headerbox{Cross-Validation of Estimates}
{name=crossval, below=results,column=1,span=1}
{
	\centering
	\includegraphics[width=.994\linewidth]{cvplot.pdf}
}

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\headerbox{Effects of Public and Elite Preferences}
{name=lateral,column=2,span=1}
{
\centering
\begin{tabular}{@{}c@{ }c@{ }c@{ }c@{}@{ }@{ }c@{ }c@{ }c@{ }c@{ }}
	\includegraphics[width=.5\linewidth]{predprobmood.pdf}&
	\includegraphics[width=.5\linewidth]{predprobconstraint.pdf}
\end{tabular}
}


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\headerbox{Effects of Support by Elected Officials}
{name=vertical,below=lateral,column=2,span=1}
{
	\centering
	\begin{tabular}{@{}c@{ }c@{ }c@{ }c@{}@{ }@{ }c@{ }c@{ }c@{ }c@{ }}
		\includegraphics[width=.5\linewidth]{medplot.pdf}&
		\includegraphics[width=.5\linewidth]{jcsplot.pdf}
	\end{tabular}
}

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\headerbox{Measures of Model Fit}{name=sepplot,column=2,below=vertical,span=1}
{   	\vspace{1mm} 
	\centering
	\begin{tabular}{c}
	\textbf{Separation Plots}\\
	Lateral Cases\\ 
	\includegraphics[height=10mm,width=80mm]{sepplot1.pdf}\\
	Vertical Cases \\ 
	\includegraphics[height=10mm,width=80mm]{sepplot2.pdf}\\
	\\
   \end{tabular}
\\
	\textbf{ROC Curve}\\
	\includegraphics[width=.7\linewidth]{roccurve.pdf}\\
}

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\headerbox{Extension: Case Salience and Invalidation}
{name=extension,column=3,span=1}
{\vspace{2mm} 
	\begin{adjustwidth}{2mm}{2mm}
		 I extend Hall's model by including additional independent variable: the \textbf{salience of cases}. If a case attracts public attention, such a salience can influence judicial decision-making since the Court is partly constrained by public opinion. I hypothesize that the effect of salience is prominent only in lateral cases, and the result is consistent with my hypothesis. 
	\end{adjustwidth}
	\includegraphics[width=.9\linewidth]{salplot.pdf}

}


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\headerbox{Problems Inherent in Hall's Model}
{name=conclusion,column=3,row=1,span=1,below=extension}
{\vspace{2mm}	
	\begin{adjustwidth}{2mm}{2mm}
	\begin{itemize}
		\item \textbf{Misspecification} \vspace{1mm}
		\\Huge difference between classical and robust standard error (especially in \textit{institutional constraint} variable in lateral cases) (King and Roberts 2014)
	\end{itemize}
\begin{tabular}{ccccc}
	& & & & \\
	\hline
	& Estimate & \textbf{SE} & $z$ value & $p$-value\\ \hline
	Classical SE & -135.54 & \textbf{153.89} & -0.881 & 0.378\\
	Robust SE & -135.54 & \textbf{46.46} & -2.917 & 0.004\\
	\hline
\end{tabular}
	\begin{itemize}
		\item[]
		\item \textbf{Institutional Constraint Variable:} Skewed \\ Distributions of Data and Standardized Residuals
	\end{itemize}

	\begin{tabular}{@{}c@{ }c@{ }c@{ }c@{}@{ }@{ }c@{ }c@{ }c@{ }c@{ }}
		\centering
		\hspace{6mm}\includegraphics[width=.4\linewidth]{histogram.pdf}&
		\includegraphics[width=.4\linewidth]{residualplot.pdf}
	\end{tabular}
\begin{itemize}
	\item \textbf{One Counterintuitive Finding} \vspace{1mm}
	\\ Hall expects a negative effect of \textbf{predicted support by the pivotal legislator} on the invalidation in vertical cases, but his finding shows the opposite, which undermines his theoretical argument (see the left plot of ``Effects of Support by Elected Official"). Also, despite the significance of this variable, original paper does not present it in the result table (by mistake).
\end{itemize}
\end{adjustwidth}
\vspace{1mm}
	
}



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